Geodesic
Optimal transport with Coulomb cost. Approximation and duality
De Pascale, Luigi1 
1 Dipartimento di Matematica, Università di Pisa, Largo Bruno Pontecorvo 5, 56127 Pisa, Italy.
ESAIM: Mathematical Modelling and Numerical Analysis , Optimal Transport, Tome 49 (2015) no. 6, pp. 1643-1657

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We revisit the duality theorem for multimarginal optimal transportation problems. In particular, we focus on the Coulomb cost. We use a discrete approximation to prove equality of the extremal values and some careful estimates of the approximating sequence to prove existence of maximizers for the dual problem (Kantorovich’s potentials). Finally we observe that the same strategy can be applied to a more general class of costs and that a classical results on the topic cannot be applied here.

Reçu le :
DOI : 10.1051/m2an/2015035
Classification : 49J45, 49N15, 49K30
Keywords: Multimarginal optimal transportation, Monge−Kantorovich problem, duality theory, Coulomb cost

De Pascale, Luigi 1

1 Dipartimento di Matematica, Università di Pisa, Largo Bruno Pontecorvo 5, 56127 Pisa, Italy. 
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     title = {Optimal transport with {Coulomb} cost. {Approximation} and duality},
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De Pascale, Luigi. Optimal transport with Coulomb cost. Approximation and duality. ESAIM: Mathematical Modelling and Numerical Analysis , Optimal Transport, Tome 49 (2015) no. 6, pp. 1643-1657. doi: 10.1051/m2an/2015035

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